A day after dropping his Senate bid, Mayor Giuliani insisted yesterday that he “wanted the job” and was “ready to do” the some of the same things he did as the Big Apple’s CEO.

“I wanted the job. I felt that I could carry on many of the things I had done as mayor of New York City in that job and spread it to the whole state,” the mayor told Tim Russert of NBC’s “Meet the Press” in an interview to air at 10:30 a.m. today.

In comments that rebut the theory his heart wasn’t in the race because he didn’t really want the job, Giuliani said he could have brought a lot to the role of New York’s junior senator.

“I feel that a lot of what I have accomplished [as mayor] … the good things that I have accomplished in the job, come out of a fairly consistent philosophy of how government inter-reacts with people, which easily applies itself to the state, to the nation,” he said.

“So I was looking forward to it. I had prepared myself for it. And I was ready to do it. I wanted to do it.”

Long Island Rep. Rick Lazio, who jumped into the Senate race after Giuliani bowed out, will be interviewed live on the show this morning.

Other than taping the interview with Russert, Giuliani maintained a low profile yesterday, with no public appearances.

The mayor turns 56 next Sunday, amid the most tumultuous time of his life.

In the short space of three weeks, Giuliani has dropped out of the Senate race to battle prostate cancer, announced his planned separation from wife Donna Hanover, and admitted he has a new relationship with Upper East Side divorcee Judith Nathan.

While the mayor said he would deal with his health problem before turning to politics, he apparently still hadn’t decided on a cancer treatment as of yesterday.

Sources told The Post that Nathan cried her eyes out while watching Giuliani’s news conference on TV Friday.

She was taken to Manhattan Eye, Ear and Throat Hospital, where the mayor rushed to her side. Mayoral aides refused comment.

Taking her dog for a late-afternoon walk outside her East 94th Street building yesterday, Nathan laughed off a reporter’s question about whether she’d hurt her eye crying.

“It’s just a normal part of things that can happen to the eye,” she said, without confirming that she’d sustained a tear-related injury.

Asked about Giuliani’s Senate shocker, Nathan said, “My only concern at this point is for the mayor’s rapid and complete recovery.”

Friends and allies of the mayor said anyone counting him out of politics is making a big mistake.

“With a record of success so unprecedented, his future is limitless,” said pollster Frank Luntz.

At City Hall, meanwhile, aides said Giuliani doesn’t intend to be a do-nothing lame duck in his final months in office.

“We are looking forward to the next 18 months of running the government in a laser-like fashion … and expanding what we have do so that all New Yorkers understand and will be uplifted by what we do,” said Deputy Mayor Joseph Lhota.

Tomorrow, the mayor is scheduled to give the keynote address at a Forbes CEO breakfast, hosted by Steve Forbes, at the Grand Hyatt Hotel.